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Chords of meanpop

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Below are listed the dyadic chords of 11-limit meanpop temperament. Meanpop is one of the two extensions of septimal meantone, which itself is the main extension of 5-limit meantone; this is the temperament tempering out 81/80, 126/125 and 385/384. Typing the chords requires consideration of the fact that meanpop conflates 9/8 and 10/9; if a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 9/8 and 16/9.

Chords requiring tempering only by 81/80 are labeled didymic, by 126/125 starling, by 225/224 marvel, by 385/384 keenanismic and by 540/539 swetismic. Chords which require any two of 81/80, 126/125 or 225/224 are labeled erato, and any two of 225/224, 385/384 or 540/539 unimarv. A chord requiring both of 81/80 and 540/539 is labeled terpsichore, and a chord requiring any three independent commas from those discussed above is labeled meanpop.

Meanpop has MOS of size 5, 7, 12, 19, 31, 50 and 81. While 5-limit meantone has been thoroughly explored, the same is not true of meanpop. The 19 note MOS would seem to be a good place to start such explorations.

Triads

Number
 Chord
 Transversal
 Type
1
 0-1-2
 1-3/2-9/8
 ambitonal
2
 0-1-3
 1-3/2-5/3
 otonal
3
 0-2-3
 1-10/9-5/3
 utonal
4
 0-1-4
 1-3/2-5/4
 otonal
5
 0-2-4
 1-9/8-5/4
 otonal
6
 0-3-4
 1-5/3-5/4
 utonal
7
 0-2-6
 1-9/8-7/5
 marvel
8
 0-3-6
 1-5/3-7/5
 starling
9
 0-4-6
 1-5/4-7/5
 marvel
10
 0-2-8
 1-10/9-14/9
 otonal
11
 0-4-8
 1-5/4-14/9
 marvel
12
 0-6-8
 1-7/5-14/9
 utonal
13
 0-1-9
 1-3/2-7/6
 otonal
14
 0-3-9
 1-5/3-7/6
 otonal
15
 0-6-9
 1-7/5-7/6
 utonal
16
 0-8-9
 1-14/9-7/6
 utonal
17
 0-1-10
 1-3/2-7/4
 otonal
18
 0-2-10
 1-9/8-7/4
 otonal
19
 0-4-10
 1-5/4-7/4
 otonal
20
 0-6-10
 1-7/5-7/4
 utonal
21
 0-8-10
 1-14/9-7/4
 utonal
22
 0-9-10
 1-7/6-7/4
 utonal
23
 0-3-13
 1-5/3-16/11
 keenanismic
24
 0-4-13
 1-5/4-16/11
 keenanismic
25
 0-9-13
 1-7/6-16/11
 keenanismic
26
 0-10-13
 1-7/4-16/11
 keenanismic
27
 0-1-14
 1-3/2-12/11
 utonal
28
 0-4-14
 1-5/4-12/11
 keenanismic
29
 0-6-14
 1-7/5-12/11
 swetismic
30
 0-8-14
 1-14/9-12/11
 swetismic
31
 0-10-14
 1-7/4-12/11
 keenanismic
32
 0-13-14
 1-16/11-12/11
 otonal
33
 0-1-15
 1-3/2-18/11
 utonal
34
 0-2-15
 1-9/8-18/11
 utonal
35
 0-6-15
 1-7/5-18/11
 swetismic
36
 0-9-15
 1-7/6-18/11
 swetismic
37
 0-13-15
 1-16/11-18/11
 otonal
38
 0-14-15
 1-12/11-18/11
 otonal
39
 0-2-17
 1-10/9-20/11
 utonal
40
 0-3-17
 1-5/3-20/11
 utonal
41
 0-4-17
 1-5/4-20/11
 utonal
42
 0-8-17
 1-14/9-20/11
 swetismic
43
 0-9-17
 1-7/6-20/11
 swetismic
44
 0-13-17
 1-16/11-20/11
 otonal
45
 0-14-17
 1-12/11-20/11
 otonal
46
 0-15-17
 1-18/11-20/11
 otonal
47
 0-6-23
 1-7/5-14/11
 utonal
48
 0-8-23
 1-14/9-14/11
 utonal
49
 0-9-23
 1-7/6-14/11
 utonal
50
 0-10-23
 1-7/4-14/11
 utonal
51
 0-13-23
 1-16/11-14/11
 otonal
52
 0-14-23
 1-12/11-14/11
 otonal
53
 0-15-23
 1-18/11-14/11
 otonal
54
 0-17-23
 1-20/11-14/11
 otonal

Tetrads

Number
 Chord
 Transversal
 Type
1
 0-1-2-3
 1-3/2-9/8-5/3
 didymic
2
 0-1-2-4
 1-3/2-9/8-5/4
 otonal
3
 0-1-3-4
 1-3/2-5/3-5/4
 ambitonal
4
 0-2-3-4
 1-10/9-5/3-5/4
 utonal
5
 0-2-3-6
 1-9/8-5/3-7/5
 erato
6
 0-2-4-6
 1-9/8-5/4-7/5
 erato
7
 0-3-4-6
 1-5/3-5/4-7/5
 erato
8
 0-2-4-8
 1-9/8-5/4-14/9
 erato
9
 0-2-6-8
 1-9/8-7/5-14/9
 erato
10
 0-4-6-8
 1-5/4-7/5-14/9
 erato
11
 0-1-3-9
 1-3/2-5/3-7/6
 otonal
12
 0-3-6-9
 1-5/3-7/5-7/6
 starling
13
 0-6-8-9
 1-7/5-14/9-7/6
 utonal
14
 0-1-2-10
 1-3/2-9/8-7/4
 otonal
15
 0-1-4-10
 1-3/2-5/4-7/4
 otonal
16
 0-2-4-10
 1-9/8-5/4-7/4
 otonal
17
 0-2-6-10
 1-9/8-7/5-7/4
 marvel
18
 0-4-6-10
 1-5/4-7/5-7/4
 marvel
19
 0-2-8-10
 1-9/8-14/9-7/4
 didymic
20
 0-4-8-10
 1-5/4-14/9-7/4
 marvel
21
 0-6-8-10
 1-7/5-14/9-7/4
 utonal
22
 0-1-9-10
 1-3/2-7/6-7/4
 ambitonal
23
 0-6-9-10
 1-7/5-7/6-7/4
 utonal
24
 0-8-9-10
 1-14/9-7/6-7/4
 utonal
25
 0-3-4-13
 1-5/3-5/4-16/11
 keenanismic
26
 0-3-9-13
 1-5/3-7/6-16/11
 keenanismic
27
 0-4-10-13
 1-5/4-7/4-16/11
 keenanismic
28
 0-9-10-13
 1-7/6-7/4-16/11
 keenanismic
29
 0-1-4-14
 1-3/2-5/4-12/11
 keenanismic
30
 0-4-6-14
 1-5/4-7/5-12/11
 unimarv
31
 0-4-8-14
 1-5/4-14/9-12/11
 unimarv
32
 0-6-8-14
 1-7/5-14/9-12/11
 terpsichore
33
 0-1-10-14
 1-3/2-7/4-12/11
 keenanismic
34
 0-4-10-14
 1-5/4-7/4-12/11
 keenanismic
35
 0-6-10-14
 1-7/5-7/4-12/11
 unimarv
36
 0-8-10-14
 1-14/9-7/4-12/11
 unimarv
37
 0-4-13-14
 1-5/4-16/11-12/11
 keenanismic
38
 0-10-13-14
 1-7/4-16/11-12/11
 keenanismic
39
 0-1-2-15
 1-3/2-9/8-18/11
 utonal
40
 0-2-6-15
 1-9/8-7/5-18/11
 unimarv
41
 0-1-9-15
 1-3/2-7/6-18/11
 swetismic
42
 0-6-9-15
 1-7/5-7/6-18/11
 swetismic
43
 0-9-13-15
 1-7/6-16/11-18/11
 unimarv
44
 0-1-14-15
 1-3/2-12/11-18/11
 ambitonal
45
 0-6-14-15
 1-7/5-12/11-18/11
 swetismic
46
 0-13-14-15
 1-16/11-12/11-18/11
 otonal
47
 0-2-3-17
 1-10/9-5/3-20/11
 utonal
48
 0-2-4-17
 1-10/9-5/4-20/11
 utonal
49
 0-3-4-17
 1-5/3-5/4-20/11
 utonal
50
 0-2-8-17
 1-9/8-14/9-20/11
 terpsichore
51
 0-4-8-17
 1-5/4-14/9-20/11
 unimarv
52
 0-3-9-17
 1-5/3-7/6-20/11
 swetismic
53
 0-8-9-17
 1-14/9-7/6-20/11
 swetismic
54
 0-3-13-17
 1-5/3-16/11-20/11
 keenanismic
55
 0-4-13-17
 1-5/4-16/11-20/11
 keenanismic
56
 0-9-13-17
 1-7/6-16/11-20/11
 unimarv
57
 0-4-14-17
 1-5/4-12/11-20/11
 keenanismic
58
 0-8-14-17
 1-14/9-12/11-20/11
 swetismic
59
 0-13-14-17
 1-16/11-12/11-20/11
 otonal
60
 0-2-15-17
 1-9/8-18/11-20/11
 didymic
61
 0-9-15-17
 1-7/6-18/11-20/11
 terpsichore
62
 0-13-15-17
 1-16/11-18/11-20/11
 otonal
63
 0-14-15-17
 1-12/11-18/11-20/11
 otonal
64
 0-6-8-23
 1-7/5-14/9-14/11
 utonal
65
 0-6-9-23
 1-7/5-7/6-14/11
 utonal
66
 0-8-9-23
 1-14/9-7/6-14/11
 utonal
67
 0-6-10-23
 1-7/5-7/4-14/11
 utonal
68
 0-8-10-23
 1-14/9-7/4-14/11
 utonal
69
 0-9-10-23
 1-7/6-7/4-14/11
 utonal
70
 0-9-13-23
 1-7/6-16/11-14/11
 keenanismic
71
 0-10-13-23
 1-7/4-16/11-14/11
 keenanismic
72
 0-6-14-23
 1-7/5-12/11-14/11
 swetismic
73
 0-8-14-23
 1-14/9-12/11-14/11
 swetismic
74
 0-10-14-23
 1-7/4-12/11-14/11
 keenanismic
75
 0-13-14-23
 1-16/11-12/11-14/11
 otonal
76
 0-6-15-23
 1-7/5-18/11-14/11
 swetismic
77
 0-9-15-23
 1-7/6-18/11-14/11
 swetismic
78
 0-13-15-23
 1-16/11-18/11-14/11
 otonal
79
 0-14-15-23
 1-12/11-18/11-14/11
 otonal
80
 0-8-17-23
 1-14/9-20/11-14/11
 swetismic
81
 0-9-17-23
 1-7/6-20/11-14/11
 swetismic
82
 0-13-17-23
 1-16/11-20/11-14/11
 otonal
83
 0-14-17-23
 1-12/11-20/11-14/11
 otonal
84
 0-15-17-23
 1-18/11-20/11-14/11
 otonal

Pentads

Number
 Chord
 Transversal
 Type
1
 0-1-2-3-4
 1-3/2-9/8-5/3-5/4
 didymic
2
 0-2-3-4-6
 1-9/8-5/3-5/4-7/5
 erato
3
 0-2-4-6-8
 1-9/8-5/4-7/5-14/9
 erato
4
 0-1-2-4-10
 1-3/2-9/8-5/4-7/4
 otonal
5
 0-2-4-6-10
 1-9/8-5/4-7/5-7/4
 erato
6
 0-2-4-8-10
 1-9/8-5/4-14/9-7/4
 erato
7
 0-2-6-8-10
 1-9/8-7/5-14/9-7/4
 erato
8
 0-4-6-8-10
 1-5/4-7/5-14/9-7/4
 erato
9
 0-6-8-9-10
 1-7/5-14/9-7/6-7/4
 utonal
10
 0-4-6-8-14
 1-5/4-7/5-14/9-12/11
 meanpop
11
 0-1-4-10-14
 1-3/2-5/4-7/4-12/11
 keenanismic
12
 0-4-6-10-14
 1-5/4-7/5-7/4-12/11
 unimarv
13
 0-4-8-10-14
 1-5/4-14/9-7/4-12/11
 unimarv
14
 0-6-8-10-14
 1-7/5-14/9-7/4-12/11
 meanpop
15
 0-4-10-13-14
 1-5/4-7/4-16/11-12/11
 keenanismic
16
 0-2-3-4-17
 1-10/9-5/3-5/4-20/11
 utonal
17
 0-2-4-8-17
 1-9/8-5/4-14/9-20/11
 meanpop
18
 0-3-4-13-17
 1-5/3-5/4-16/11-20/11
 keenanismic
19
 0-3-9-13-17
 1-5/3-7/6-16/11-20/11
 unimarv
20
 0-4-8-14-17
 1-5/4-14/9-12/11-20/11
 unimarv
21
 0-4-13-14-17
 1-5/4-16/11-12/11-20/11
 keenanismic
22
 0-9-13-15-17
 1-7/6-16/11-18/11-20/11
 meanpop
23
 0-13-14-15-17
 1-16/11-12/11-18/11-20/11
 otonal
24
 0-6-8-9-23
 1-7/5-14/9-7/6-14/11
 utonal
25
 0-6-8-10-23
 1-7/5-14/9-7/4-14/11
 utonal
26
 0-6-9-10-23
 1-7/5-7/6-7/4-14/11
 utonal
27
 0-8-9-10-23
 1-14/9-7/6-7/4-14/11
 utonal
28
 0-9-10-13-23
 1-7/6-7/4-16/11-14/11
 keenanismic
29
 0-6-8-14-23
 1-7/5-14/9-12/11-14/11
 terpsichore
30
 0-6-10-14-23
 1-7/5-7/4-12/11-14/11
 unimarv
31
 0-8-10-14-23
 1-14/9-7/4-12/11-14/11
 unimarv
32
 0-10-13-14-23
 1-7/4-16/11-12/11-14/11
 keenanismic
33
 0-6-9-15-23
 1-7/5-7/6-18/11-14/11
 swetismic
34
 0-9-13-15-23
 1-7/6-16/11-18/11-14/11
 unimarv
35
 0-6-14-15-23
 1-7/5-12/11-18/11-14/11
 swetismic
36
 0-13-14-15-23
 1-16/11-12/11-18/11-14/11
 otonal
37
 0-8-9-17-23
 1-14/9-7/6-20/11-14/11
 swetismic
38
 0-9-13-17-23
 1-7/6-16/11-20/11-14/11
 unimarv
39
 0-8-14-17-23
 1-14/9-12/11-20/11-14/11
 swetismic
40
 0-13-14-17-23
 1-16/11-12/11-20/11-14/11
 otonal
41
 0-9-15-17-23
 1-7/6-18/11-20/11-14/11
 terpsichore
42
 0-13-15-17-23
 1-16/11-18/11-20/11-14/11
 otonal
43
 0-14-15-17-23
 1-12/11-18/11-20/11-14/11
 otonal

Hexads

Number
 Chord
 Transversal
 Type
1
 0-2-4-6-8-10
 1-9/8-5/4-7/5-14/9-7/4
 erato
2
 0-4-6-8-10-14
 1-5/4-7/5-14/9-7/4-12/11
 meanpop
3
 0-6-8-9-10-23
 1-7/5-14/9-7/6-7/4-14/11
 utonal
4
 0-6-8-10-14-23
 1-7/5-14/9-7/4-12/11-14/11
 meanpop
5
 0-9-13-15-17-23
 1-7/6-16/11-18/11-20/11-14/11
 meanpop
6
 0-13-14-15-17-23
 1-16/11-12/11-18/11-20/11-14/11
 otonal